The ionic strength of a

solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solutio ...

is a measure of the

concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', ''number concentration'', ...

of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total

electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon ...

concentration in solution will affect important properties such as the

dissociation constant In chemistry, biochemistry, and pharmacology, a dissociation constant (K_D) is a specific type of equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a complex ...

or the

solubility In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...

of different salts. One of the main characteristics of a solution with dissolved ions is the ionic strength. Ionic strength can be molar (mol/L solution) or molal (mol/kg solvent) and to avoid confusion the units should be stated explicitly. The concept of ionic strength was first introduced by Lewis and

Randall Randall may refer to the following: Places United States *Randall, California, former name of White Hall, California, an unincorporated community * Randall, Indiana, a former town *Randall, Iowa, a city *Randall, Kansas, a city *Randall, Minnesot ...

in 1921 while describing the

activity coefficient In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same ...

s of strong electrolytes.

Quantifying ionic strength

The molar ionic strength, ''I'', of a solution is a function of the

of ''all'' ions present in that

. :

I = \begin\frac\end\sum_^ c_i z_i^

where one half is because we are including both

cation An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...

s and

anion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...

s, ''c''_i is the molar concentration of ion i (M, mol/L), ''z''_i is the charge number of that ion, and the sum is taken over all ions in the solution. For a 1:1

such as

sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35. ...

, where each ion is singly-charged, the ionic strength is equal to the concentration. For the electrolyte MgSO₄, however, each ion is doubly-charged, leading to an ionic strength that is four times higher than an equivalent concentration of sodium chloride: :

I = \frac (+2)^2+c(-2)^2 = \frac c + 4c = 4c

Generally multivalent ions contribute strongly to the ionic strength.

Calculation example

As a more complex example, the ionic strength of a mixed solution 0.050 M in Na₂SO₄ and 0.020 M in KCl is: :

\\ & = 0.17 M \end

Non-ideal solutions

Because in non- ideal solutions volumes are no longer strictly additive it is often preferable to work with

molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...

''b'' (mol/kg of H₂O) rather than molarity ''c'' (mol/L). In that case, molal ionic strength is defined as: :

I = \frac\sum_^ b_z_^

in which :''i'' = ion identification number :''z'' = charge of ion :''b'' = molality (mol solute per Kg solvent)

Importance

The ionic strength plays a central role in the

Debye–Hückel theory The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized Poisson–Boltzmann model, which assumes an extrem ...

that describes the strong deviations from ideality typically encountered in ionic solutions. It is also important for the theory of double layer and related electrokinetic phenomena and electroacoustic phenomena in colloids and other

heterogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...

systems. That is, the Debye length, which is the inverse of the Debye parameter (''κ''), is inversely proportional to the square root of the ionic strength. Both molar and molal ionic strength have been used, often without explicit definition. Debye length is characteristic of the double layer thickness. Increasing the concentration or valence of the

counterion 160px, Polystyrene sulfonate, a cation-exchange resin, is typically supplied with as the counterion.">cation-exchange_resin.html" ;"title="Polystyrene sulfonate, a cation-exchange resin">Polystyrene sulfonate, a cation-exchange resin, is typical ...

s compresses the double layer and increases the electrical potential

gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...

. Media of high ionic strength are used in stability constant determination in order to minimize changes, during a titration, in the activity quotient of solutes at lower concentrations. Natural waters such as mineral water and

seawater Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L, 35 ppt, 600 mM). This means that every kilogram (roughly one liter by volume) of seawater has appro ...

have often a non-negligible ionic strength due to the presence of dissolved salts which significantly affects their properties.

External links

Ionic strength

Ionic strength introduction at the EPA web site

References